How to find zero-state step response from a discrete time system?

I have a discrete time system as such: y[n] = 0.8y[n-1]-0.64y[n-2]+0.866x[n]

I would like to learn how I can compute the the zero-state step response of this system for 0<=n<=49. I am struggling because I am required to do so without the use of built-in functions. Any guidance would be appreciated.

Answer 1

[Jonas]

if you are interested in the step response, your x(n) is 0 for n<0 and 1 else. y(n) is 0 for n<0. just iterate with a for loop for n=1:49 and calculate y(n)

start with e.g. n=0 y(0)=0.8*y(-1)-0.64*y(-2)+0.866*x(0)

which in this case everything is zeros except the last part of the expression go on from there at calculate y(1)